Package 'zeroEQpart'

Zero Order vs (Semi) Partial Correlation Test and CI

Description

Calculate the statistical significance of a zero order correlation being equal to a partial or semi-partial correlation using the bias-corrected and accelerated bootstrap method from "An Introduction to the Bootstrap" Efron (1983) <0-412-04231-2>. Confidence intervals for the parameter (zero order minus partial) can also be determined.

pzcor

The pzcor function tests one of the following null hypotheses:

• $\rho.xy - \rho.xy.z = 0$ (default)

• $\rho.xy - \rho.xy.z \ge 0$

• $\rho.xy - \rho.xy.z \le 0$

See pzcor for details.

pzconf

The pzconf function computes confidence intervals for the parameter: $\rho.xy - \rho.xy.z$. To be used with pzcor. See pzconf for details.

Author(s)

Maintainer: Dan Richard [email protected]

Other contributors:

• Karen Buro [email protected] [contributor]

• Wanhua Su [email protected] [contributor]

See Also

Useful links:

• https://github.com/djrichar92/zeroEQpart

• Report bugs at https://github.com/djrichar92/zeroEQpart/issues

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Calculate Confidence Intervals for the Difference of Zero Order and (Semi) Partial Correlation

Description

The pzconf function calculates confidence intervals for a zero order correlation minus a (semi) partial correlation ($\rho.xy - \rho.xy.z$). It is intended to be used after the pzcor function.

Usage

pzconf(pzcor_obj, level = 0.9)

Arguments

pzcor_obj	pzcor object (output from pzcor function).
level	numerical. Confidence level used to calculate the confidence interval. This may be a vector so multiple intervals can be determined.

Details

The pzconf function calculates confidence intervals based on the bootstrap distribution determined from the pzcor function. See ?pzcor for details.

Value

The confidence interval(s) is(are) displayed in a dataframe with four columns: Level, Lower, Upper, and Warnings. Level refers to the confidence level of the interval. Lower and Upper are the respective lower and upper bounds of the interval. Warnings may say "Max Level Passed" to show that the specified confidence level exceeds the largest confidence interval that can be determined from the test. The largest confidence interval is shown in the last row (named "Max").

See Also

pzcor

Examples

require(graphics)
require(MASS)
# data
set.seed(1111)
mu <- rep(0,4)
Sigma <- matrix(.2, nrow=4, ncol=4) + diag(4)*.8
data <- mvrnorm(n=100, mu=mu, Sigma=Sigma)

# p.(1,2) = p.(1,2)|(3,4) test
test <- pzcor(data[,1], data[,2], data[,c(3,4)], k = 2000)
hist(test$distribution)
pzconf(test, c(0.9, 0.95, 0.99))

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Test for Equal Zero Order and (Semi) Partial Correlation

Description

Compute a bootstrap test to determine whether zero order correlation is equal to partial or semi-partial correlation.

Usage

pzcor(x, y, z, semi = FALSE, k = 1000, method = "pearson",
  test = "eq")

Arguments

x	a numeric vector.
y	a numeric vector.
z	a numeric vector (data.frame, matrix, etc.)
semi	logical. If TRUE, then the semi-partial correlation between x and y given z is used. If FALSE (default), then the partial correlation between x given z and y given z is used.
k	the number of bootstrap samples taken (default is 1000).
method	a character string indicating which correlation coefficient is to be computed. One of "pearson" (default), "kendall", or "spearman" can be abbreviated.
test	character string denoting the null hypothesis to be tested. Can be one of the three: 'eq' tests $\rho.xy - \rho.xy.z = 0$ (default) 'gt' tests $\rho.xy - \rho.xy.z \ge 0$ 'lt' tests $\rho.xy - \rho.xy.z \le 0$

Details

Uses the bias-corrected and accelerated (BCa) bootstrap method to test if the difference $\rho.xy - \rho.xy.z$ is equal to, above, or below zero where $\rho.xy$ is the zero order correlation between variables $x$ and $y$, and $\rho.xy.z$ is the (semi) partial correlation between the respective variables after partialing out variables represented by $z$.

If the bootstrap distribution of $\rho.xy - \rho.xy.z$ is strictly above or below zero, then the p-value provided is the most extreme value that can be determined by the test. In the case of highly correlated variables, the covariance matrix may be singular which will lead to k_eff being less than k (as $\rho.xy - \rho.xy.z$ would not be computed).

Value

acceleration	the acceleration used for the BCa method.
alpha	the proportion of the bootstrapped distribution below zero.
bias	the bias used for the BCa method.
call	shows the function call.
difference	calculated from the data. Same as p.xy - p.xy.z.
distribution	the estimated distribution of the difference as determined through bootstrapping.
k_eff	the number of successful bootstrap samples. Less than or equal to k.
method	the method of correlation used.
p.value	significance level of the test.
p.xy	Zero order correlation between x and y.
p.xy.z	(semi) partial correlation between x and y while accounting for z.
semi	logical. If TRUE, p.xy.z is the semi-partial correlation. Otherwise p.xy.z is the partial correlation.
test	shows the type of test performed.

See Also

pzconf

Examples

require(graphics)
require(MASS)
# data
set.seed(1111)
mu <- rep(0,4)
Sigma <- matrix(.2, nrow=4, ncol=4) + diag(4)*.8
data <- mvrnorm(n=100, mu=mu, Sigma=Sigma)

# p.(1,2) = p.(1,2)|(3,4) test
test <- pzcor(data[,1], data[,2], data[,c(3,4)], k = 2000, semi = FALSE,
              test = 'eq')
hist(test$distribution)
test

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